{
  "id": "2106.09126",
  "version": "v1",
  "published": "2021-06-16T20:56:22.000Z",
  "updated": "2021-06-16T20:56:22.000Z",
  "title": "The minimal ramification problem for rational function fields over finite fields",
  "authors": [
    "Lior Bary-Soroker",
    "Alexei Entin",
    "Arno Fehm"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of number fields, which we establish for abelian, symmetric and alternating groups in many cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-16T20:56:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F12",
      "11R32",
      "11S15",
      "11R58"
    ],
    "keywords": [
      "rational function fields",
      "minimal ramification problem",
      "finite fields",
      "prescribed finite galois group",
      "general conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}